Filters, Physics tutorial

Introduction:

Filter is the electrical network which modifies amplitude and/or phase characteristics of the signal with respect to frequency. Preferably, filter won't add new frequencies to input signal, nor will it change component frequencies of that signal, but it will adjust relative amplitudes of different frequency components and/or their phase relationships.

All filters irrespective of kind and response should have the electrical layout that is referred to as topology of filter. Certain filter kinds and frequency responses can only be accommodated by specific filter topologies. The bandpass filter can never be accommodated by the L-filter topology.

The common need for filter circuits is in high-performance stereo systems, where definite ranges of audio frequencies require be amplifying or suppressing for best sound quality and power efficiency. Equalizers permit amplitudes of numerous frequency ranges to be adjusted to suit listener's taste and acoustic properties of listening area. Crossover networks block certain ranges of frequencies from reaching speakers.

Filter topology:

Topology of the electronic circuit is form taken by network of interconnections of circuit components. Various specific values or ratings of components are considered as being same topology. Topology is not concerned with physical outline of components in the circuit, nor with their positions on the circuit diagram. It is only concerned with what connections are present between components.

Electronic filter topology states electronic filter circuits without taking note of values of components employed but only way in which those components are joined.

Filter topologies may be divided in passive and active types. Passive topologies are made up of completely of passive components: capacitors, resistors, and inductors. Active topologies also comprise active components like transistors, op amps, and other Integrated Circuits which need power.

Topologies may be executed either in unbalanced form or in balanced form when used in balanced circuits. Implementations like electronic mixers and stereo sound may need arrays of matching circuits.

Passive topologies:

Passive filters have been long in development and use. Many are built from simple two-port networks known as sections. It should have at least one series component and one shunt component. Sections are always joined in cascade or daisy-chain topology, comprising of either repeats of same section or of entirely different sections.

Few passive filters, comprising of only one or two filter sections, are provided special names comprising L-section, T-section and Π-section that are unbalanced filters, and C-section, H-section and box-section that are balanced. All are built upon the simple ladder topology.

Active filter:

Active filter is a kind of analog electronic filter which utilizes active components like amplifier. Amplifiers comprised in filter design can be utilized to enhance performance and predictability of filter, while avoiding requirement for inductors. The amplifier prevents load impedance of following stage from affecting characteristics of filter. The active filter can have complex poles and zeros without using bulky or expensive inductor. Shape of response, Q i.e. quality factor and tuned frequency can frequently be set with low-cost variable resistors. In few active filter circuits, one parameter can be attuned without affecting others. Available active devices have restricted bandwidth, so they are frequently impractical at high frequencies

Single element filter:

The single inductor and single Capacitor filter is called as Single Element Topology. This signifies it has single reactance represented by Inductor or Capacitor in topology. 

1004_Single Element Filter Topology.jpg

Resonant circuit includes the Inductor and Capacitor in parallel. Placed across the input port it serves as the Band Pass Filter. Similarly the Capacitor in series with the Inductor placed in series with the input port also serves as the Band Pass Filter.

L-FILTER:

The L filter comprises of two reactive elements, one in series and one in parallel with output port:

This makes it two element filter. In High Pass Filter capacitor presents high impedance to lower frequencies while permitting higher frequencies to pass to output port. In the meantime inductor that is joined across output port shunts lower frequencies across port at the same time presenting itself as high impedance to higher frequencies thereby complementing capacitor in promoting passage of high frequencies from input port to output port.

1022_High Pass-low Pass L-Filter.jpg

Converse is true of Low pass Filter where roles of capacitor and inductor are reversed.

T filter and π filter:

Three-element filters can have T or π topology and in either of the topologies may be low-pass, high-pass, band-pass or band-stop filter. If duplicated components in filter are of the same value then it is defined as symmetrical or else it is asymmetrical. Symmetry of asymmetry of T or π filter depends on required frequency characteristics.

High-pass T filter in has very low impedance at high frequencies, and very high impedance at low frequencies. This signifies that it can be inserted in the transmission line, resulting in high frequencies being passed and low frequencies being reflected.

Also for low-pass π filter below, circuit may be joined to transmission line to transmit low frequencies and reflect high frequencies.

276_T FILTER AND π FILTER.jpg

Multiple Element Filters:

Multiple element filters topology is like a ladder derived from replicated L filter sections, T filter sections or π filter sections as more elements are generally needed to enhance certain parameter of filters like stop-band rejection or slope of transition from pass-band to stop-band.

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